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The value of $left parenthesis cosec space straight alpha space minus space sin space straight alpha right parenthesis space space left parenthesis sec space straight alpha minus cos space straight alpha right parenthesis space left parenthesis tan space straight alpha space plus space cot space straight alpha right parenthesis$

144 Views

72.

If x = a sin θ - b cos θ, y = a cos θ + b sin θ, then which of the following is true?

$straight x squared over straight y squared space plus space straight a squared over straight b squared space equals space 1$
$straight x squared space plus space straight y squared space equals space straight a squared space minus space straight b squared$
$straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space 1$
$straight x squared over straight a squared space plus space straight y squared over straight b squared space equals space 1$

351 Views

73.

The value of
cot 41°. cot 42°. cot 43°. cot 44°. cot 45°. cot 46°. cot 47°. cot 48°. cot 49°.

439 Views

74.
If tan A = n tan B and sin A = m sin B, then the value of cos²A is

$fraction numerator straight m squared minus 1 over denominator straight n squared plus 1 end fraction$
$fraction numerator straight m squared plus 1 over denominator straight n squared minus 1 end fraction$
$fraction numerator straight m squared plus 1 over denominator straight n squared plus 1 end fraction$
$fraction numerator straight m squared plus 1 over denominator straight n squared plus 1 end fraction$

fraction numerator straight m squared plus 1 over denominator straight n squared plus 1 end fraction

tan A = n tan B
or
cot B = n cotA ...(i)
sin A = m sin B
or
cosec B = m cosec A ...(ii)
(ii)² - (i)²cosec² B - cot² B = m²cosec² A - n² cot²A
$1 space equals space fraction numerator straight m squared over denominator sin squared straight A end fraction minus fraction numerator straight n squared cos squared straight A over denominator sin squared straight A end fraction 1 space equals space fraction numerator straight m squared minus straight n squared cos squared straight A over denominator sin squared straight A end fraction$
$rightwards double arrow space space sin squared straight A space equals space straight m squared minus straight n squared cos squared straight A rightwards double arrow 1 minus cos squared straight A space equals space straight m squared minus straight n squared cos squared straight A rightwards double arrow space space straight n squared cos squared straight A minus cos squared straight A space equals space straight m squared minus 1 rightwards double arrow space space cos squared straight A left parenthesis straight n squared minus 1 right parenthesis space equals space straight m squared minus 1 rightwards double arrow space space space cos squared straight A space equals space fraction numerator straight m squared minus 1 over denominator straight n squared minus 1 end fraction$

239 Views

75.

The value of the expression
(1 + sec 22° + cot 68°) (1 - cosec 22° + tan 68°) is

0
1
-1
-1

1505 Views

76.

If $straight x space sin cubed straight theta space plus space straight y space cos cubed straight theta space equals space space sin space straight theta space cos space straight theta$ and $straight x space sin space straight theta space minus space straight y space cos space straight theta equals space space 0 comma$ then the value of $left parenthesis straight x squared plus straight y squared right parenthesis$ equals

1
$1 half$
$3 over 2$
$3 over 2$

429 Views

77.

If $sec space straight theta space space plus space tan space straight theta space equals space straight m space left parenthesis greater than 1 right parenthesis comma$ then the value of $sin space straight theta$ $left parenthesis 0 degree space less than thin space straight theta space less than space 90 degree right parenthesis$ is:

$fraction numerator 1 minus straight m squared over denominator 1 plus straight m squared end fraction$
$fraction numerator straight m squared minus 1 over denominator straight m squared plus 1 end fraction$
$fraction numerator straight m squared plus 1 over denominator straight m squared minus 1 end fraction$
$fraction numerator straight m squared plus 1 over denominator straight m squared minus 1 end fraction$

509 Views

78.

If $left parenthesis straight a squared minus straight b squared right parenthesis space sin space straight theta space plus space 2 ab space cosθ space equals space straight a squared space plus space straight b squared comma space then space tanθ space equals space thin space ?$

$fraction numerator 2 ab over denominator straight a squared minus straight b squared end fraction$
$fraction numerator straight a squared minus straight b squared over denominator 2 ab end fraction$
$fraction numerator ab over denominator straight a squared minus straight b squared end fraction$
$fraction numerator ab over denominator straight a squared minus straight b squared end fraction$

419 Views

79.

If $2 straight y space cosθ space equals space straight x space sinθ$ and $2 straight x space sec space straight theta space minus space straight y space cosec space straight theta space equals space 3 comma$ then the value of $open parentheses straight x squared space plus space 4 straight y squared close parentheses$ is

762 Views

80.

The expression of
$fraction numerator cot space straight theta space plus space cosec space straight theta space minus space 1 over denominator cot space straight theta space minus space cosec space straight theta space plus space 1 end fraction$ is equal to

$fraction numerator 1 plus cos space straight theta over denominator sin space straight theta end fraction$
$fraction numerator 1 minus cos space straight theta over denominator sin space straight theta end fraction$
$fraction numerator cot space straight theta space plus space 1 over denominator cosec space straight theta end fraction$
$fraction numerator cot space straight theta space plus space 1 over denominator cosec space straight theta end fraction$